Question

On introducing a thin film in the path of one of the two interfering beams, the central fringe will shift by one fringe width. If $\mu =1.5$, the thickness of the film is (wavelength of monochromatic light is $\lambda$)

• A. $4\lambda$
• B. $3\lambda$
• C. $2\lambda$
• D. $\lambda$

Answer 1

The correct option is C

$2\lambda$

Step 1. Given data:

1. The fringe shift $\mu =1.5$
2. wavelength of monochromatic light is$=\lambda$
3. Number of fringes $n=$$1$

Step 2. Formula used:

The path difference in the path of the interfering beam due to the thin film is given by,

$\left(\mu -1\right)t=n\lambda$ (where $t=$the thickness of the film, $n=$The number of fringes shifted)

Step 3. Calculating the thickness of the film:

The thickness of the thin film can be calculated as,

$\begin{array}{rcl}\left(1.5-1\right)t& =& \lambda \\ & \Rightarrow & t=\frac{\lambda }{0.5}\\ & \Rightarrow & =2\lambda \end{array}$

Thus, the thickness of the film is$2\lambda$

Hence, option C is the correct answer.